value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

AREA, How do you find the distributive property any faster?

How do you find the distributive property any faster?

Find the sum of first 40 positive integers, Find the sum of first 40 positi...

Find the sum of first 40 positive integers divisible by 6 also find the sum of first 20 positive integers divisible by 5 or 6. Ans:          No's which are divisible by 6 are

Four distinct points on a circle, If (a,1/a), (b,1/b),(c,1/c),(d,1/d) are f...

If (a,1/a), (b,1/b),(c,1/c),(d,1/d) are four distinct points on a circle of radius 4 units then,abcd is equal to??   Ans) As they are of form (x,1/x) let eq of circle be x

Domain and range of a function , Domain and range of a functio:  One of th...

Domain and range of a functio:  One of the more significant ideas regarding functions is that of the domain and range of a function. In simplest world the domain of function is th

Properties of the indefinite integral, Properties of the Indefinite Integra...

Properties of the Indefinite Integral 1.  ∫ k f ( x ) dx = k ∫ f ( x ) dx where k refer for any number.  Thus, we can factor multiplicative constants out of indefinite integral

Numerical methods for ordinary differential equationsordinay, #k1=f(Tn, Xn)...

#k1=f(Tn, Xn), k2=f (Tn + H.Y,Xn + H.Y.k1) Xn+1=Xn + H(a.k1+ b.k2) Find a relation between Y,a and b so that the method is second order consistent.

Standard deviation, Certain model of new home distributed with a mean of $1...

Certain model of new home distributed with a mean of $150,000. Find percentage of buyers who paid between $150,000-155,000 if standard deviation is $1800.

Find the radius and centre of a circle, Find the centre of a circle passing...

Find the centre of a circle passing through the points (6, -6), (3, -7) and (3,3).Also find the radius.

Geometry, what shapes can go into a triangular prism

what shapes can go into a triangular prism

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd